Control device for alternating-current motor

ABSTRACT

In one coordinate system of arbitrary rectangular coordinate systems including a coordinate system in which the position of a stator is fixed, a coordinate system in which the position of a rotor is fixed, and a coordinate system which rotates at a rotational frequency which is n times (n is an integer which is not 0 or 1) that of the rotor, a filter on any other coordinate system is defined. Further, driving of a motor is controlled by utilizing this filter. As a result, a coordinate transformation operation need not be individually performed with respect to control variables.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to control over a driving current which issupplied to an alternating-current motor including a rotor and a stator.

2. Description of the Related Art

A typical driving current supplied to a three phase alternating-currentmotor including a rotor and a stator is a current having three phases ofiu, iv and iw. This three-phase driving current is controlled based onan output torque command from the motor. In a heretofore commontechnique for controlling such a motor, a current having respectivephases (the respective phases of u, v and w) is converted into currentsof d and q axis coordinate systems of an exciting current axis (a daxis) and a torque current axis (a q axis), and each converted axiscurrent is controlled to match with an axis command value obtained froma torque command of the motor.

Such control assumes that a motor driving current basically conforms toa sine wave, and such control is directed at this fundamental wavecomponent only. However, in reality, a magnetic flux generated inaccordance with a motor driving current is distorted, or a higherharmonic component is generated in a motor driving current due tovarious situations such as characteristics at the time of inverterswitching or the like.

Therefore, in order to perform further accurate control, control must becarried out taking a higher harmonic component into consideration.

As a control method for a higher harmonic current as a frequencycomponent n times that of a fundamental wave component, there has beenproposed preparation of a coordinate system by which a current can beprocessed as a direct current with respect to all current components ascontrol targets and execution of control over a current transformed onthe coordinate system and a command value (See, for example, JapanesePatent Application Laid-open No. 2002-223600).

However, in the above-described art, control over a higher harmoniccurrent component is executed on a coordinate system for the higherharmonic current component. Therefore, after performing coordinatetransformation from three phases of u, v and w (an αβ phase: acoordinate system with a stator fixed) into an axis coordinate system orthe like, control or the like is performed, and an output obtained bythis control is again subjected to reverse coordinate transformation.Therefore, because many coordinate transformation operations must becarried out, calculations are undesirably complicated.

SUMMARY OF THE INVENTION

According to the present invention, a higher harmonic component can bealso controlled. Therefore, a higher harmonic wave contained in a motordriving current can be suppressed, and a copper loss can be therebyreduced. Further, by applying an appropriate higher harmonic current toa higher harmonic component contained a magnet, an increase in an outputtorque can be expected. Furthermore, because control over any coordinateaxis can be executed on a single coordinate axis, a coordinatetransformation operation need not be performed each time, therebyeffectively executing control. For example, PI control over a higherharmonic current which is n times the rotational frequency of a rotorcan be executed in a dq axis coordinate system in which the position ofthe rotor is fixed, or PI control over a dq current in the dq axiscoordinate system with the rotor fixed can be executed on an αβcoordinate system in which the position of the stator is fixed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing a configuration in a dq axis coordinate systemfor PI control over an nth-order higher harmonic wave;

FIG. 2 is a view showing another configuration in the dq axis coordinatesystem for PI control over the nth-order higher harmonic wave;

FIG. 3 is a view showing a structural example of a control system on adq axis;

FIG. 4 is a view showing a configuration in an αβ coordinate system forPI control over a dq axis current;

FIG. 5 is a view showing a structural example of a control system on αβ;

FIG. 6 is a view showing a change in a motor current on the dq axiscaused by a conventional technique;

FIG. 7 is a view showing a change in a motor current caused by atechnique with the dq axis prepared for each higher harmonic wave;

FIG. 8 is a view showing a change in a motor current caused by atechnique according to the embodiment which realizes on the dq axis thecontrol on an ef axis (n=6); and

FIG. 9 is a view showing a configuration of a higher harmonic componentin the coordinate system shown in FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A preferred embodiment of the present invention will be describedhereinafter.

“Coordinate System”

An example will be considered of a rotor which rotates at a fixedangular velocity ω and a rotation angle θ. An αβ coordinate system inwhich the position of a stator is fixed, a dq axis coordinate system inwhich the position of a is rotor fixed, and an ef axis coordinate systemrotating at a rotational velocity which is n times that of the rotorwill be introduced.

Respective state quantities (column vectors) (x_(α), x_(β)), (x_(d),x_(q)), (x_(e), x_(f)) on the αβ coordinate system, the dq axiscoordinate system and the ef axis coordinate system have the followingrelationship through a transformation matrix T(θ). $\begin{matrix}{\begin{pmatrix}x_{d} \\x_{q}\end{pmatrix} = {{T(\theta)}\begin{pmatrix}x_{\alpha} \\x_{\beta}\end{pmatrix}}} & (1) \\{\begin{pmatrix}x_{e} \\x_{f}\end{pmatrix} = {{T\left( {n\quad\theta} \right)}\begin{pmatrix}x_{\alpha} \\x_{\beta}\end{pmatrix}}} & (2) \\{{T\left( {n\quad\theta} \right)} = \begin{pmatrix}{\cos\quad n\quad\theta} & {\sin\quad n\quad\theta} \\{{- \sin}\quad n\quad\theta} & {\cos\quad n\quad\theta}\end{pmatrix}} & (3)\end{matrix}$

PI control in each coordinate system will now be prepared as follows. Itis to be noted that Kp is a constant for proportional control and Ki isa constant for integration control. Furthermore, a suffix r denotes atarget value. Moreover, in the description of this specification, samefonts may be used to denote scalars, vectors and matrices.$\begin{matrix}\left( {\alpha - {\beta\quad{Coordinate}\quad{System}}} \right) & \quad \\{\quad{\begin{pmatrix}v_{\alpha} \\v_{\beta}\end{pmatrix} = {{\begin{pmatrix}K_{p\quad\alpha} & 0 \\0 & K_{p\quad\beta}\end{pmatrix}\left\{ {\begin{pmatrix}i_{\alpha\quad r} \\i_{\beta\quad r}\end{pmatrix} - \begin{pmatrix}i_{\alpha} \\i_{\beta}\end{pmatrix}} \right\}} + {\begin{pmatrix}K_{i\quad\alpha} & 0 \\0 & K_{i\quad\beta}\end{pmatrix}\begin{pmatrix}e_{\alpha} \\e_{\beta}\end{pmatrix}}}}} & (4) \\{\quad{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{\alpha} \\e_{\beta}\end{pmatrix}} = {\begin{pmatrix}i_{\alpha\quad r} \\i_{\beta\quad r}\end{pmatrix} - \begin{pmatrix}i_{\alpha} \\i_{\beta}\end{pmatrix}}}} & (5) \\\left( {d - {q\quad{Axis}\quad{Coordinate}\quad{System}}} \right) & \quad \\{\quad{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{\begin{pmatrix}K_{p\quad d} & 0 \\0 & K_{p\quad q}\end{pmatrix}\left\{ {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\}} + {\begin{pmatrix}K_{i\quad d} & 0 \\0 & K_{i\quad q}\end{pmatrix}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}}}}} & (6) \\{\quad{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} = {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}}}} & (7) \\\left( {e - {f\quad{Axis}\quad{Coordinate}\quad{System}}} \right) & \quad \\{\quad{\begin{pmatrix}v_{e} \\v_{f}\end{pmatrix} = {{\begin{pmatrix}K_{p\quad e} & 0 \\0 & K_{p\quad f}\end{pmatrix}\left\{ {\begin{pmatrix}i_{e\quad r} \\i_{f\quad r}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}} \right\}} + {\begin{pmatrix}K_{i\quad e} & 0 \\0 & K_{if}\end{pmatrix}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}}}}} & (8) \\{\quad{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}} = {\begin{pmatrix}i_{e\quad r} \\i_{fr}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}}}} & (9)\end{matrix}$“Higher Harmonic Control in dq Axis Coordinate System (PI Control Overef Axis Coordinate System in dq Axis Coordinate System)”

The dq axis coordinate system and the ef axis coordinate system have therelationships represented by Expressions (1) and (2). Considering avoltage v, a current i and an error integration value (see Expression(5)) e of the current as state quantities, they can be expressed asfollows. It is to be noted that T′((n−1)θ) is a transposed matrix ofT((n−1)θ) and the dq axis coordinate system advances by θ with respectto αβ. Therefore, a difference in order between the both coordinatesystems is n−1. $\begin{matrix}{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}v_{e} \\v_{f}\end{pmatrix}}} & (10) \\{\begin{pmatrix}i_{d} \\i_{q}\end{pmatrix} = {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}}} & (11) \\{\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix} = {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}}} & (12)\end{matrix}$

The PI control over the ef coordinate system represented by Expressions(8) and (9) is transformed into the dq axis coordinate system byutilizing Expressions (10) to (12). $\begin{matrix}\begin{matrix}{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}K_{p\quad e} & 0 \\0 & K_{p\quad f}\end{pmatrix}{T\left( {\left( {n - 1} \right)\theta} \right)}\left\{ {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\}} +}} \\{{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}K_{i\quad e} & 0 \\0 & K_{i\quad f}\end{pmatrix}{T\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} \\{= \begin{pmatrix}{\frac{K_{pe} + K_{pf}}{2} + {\frac{K_{pe} + K_{pf}}{2}{\cos\left( {2\left( {n - 1} \right)\theta} \right)}}} & {\frac{K_{pe} + K_{pf}}{2}{\sin\left( {2\left( {n - 1} \right)\theta} \right)}} \\{\frac{K_{pe} + K_{pf}}{2}{\sin\left( {2\left( {n - 1} \right)\theta} \right)}} & {\frac{K_{pe} + K_{pf}}{2} - {\frac{K_{pe} + K_{pf}}{2}{\cos\left( {2\left( {n - 1} \right)\theta} \right)}}}\end{pmatrix}} \\{\left\{ {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\} +} \\{\begin{pmatrix}{\frac{K_{ie} + K_{if}}{2} + {\frac{K_{ie} + K_{if}}{2}{\cos\left( {2\left( {n - 1} \right)\theta} \right)}}} & {\frac{K_{ie} + K_{if}}{2}{\sin\left( {2\left( {n - 1} \right)\theta} \right)}} \\{\frac{K_{ie} + K_{if}}{2}{\sin\left( {2\left( {n - 1} \right)\theta} \right)}} & {\frac{K_{ie} + K_{if}}{2} - {\frac{K_{ie} + K_{if}}{2}{\cos\left( {2\left( {n - 1} \right)\theta} \right)}}}\end{pmatrix}} \\{\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}}\end{matrix} & (14) \\\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} = {\frac{\mathbb{d}}{\mathbb{d}t}\left\{ {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}} \right\}}} \\{= {{\frac{\mathbb{d}}{\mathbb{d}t}\left\{ {T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)} \right\}{T\left( {\left( {n - 1} \right)\theta} \right)}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} + {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}}}} \\{= {{\left( {n - 1} \right){\omega\begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix}}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} + {{T^{\prime}\left( {\left( {n - 1} \right)\theta} \right)}\left\{ {\begin{pmatrix}i_{e\quad r} \\i_{f\quad r}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}} \right\}}}} \\{= {{\left( {n - 1} \right){\omega\begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix}}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} + \begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}}}\end{matrix} & (15)\end{matrix}$

Expression (15) can be converted into Expression (17). Additionally,assuming that K_(pe)=K_(pf), K_(ie)=K_(if), Expression (16) can beobtained by organizing the above expressions. $\begin{matrix}{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{K_{pe}\left\{ {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\}} + {K_{ie}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}}}} & (16) \\{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} = {{\left( {n - 1} \right){\omega\begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix}}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} + \begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}}} & (17)\end{matrix}$

Based on a current error (i_(dr)−i_(d), i_(qr)−i_(q)) in Expression(17), a transfer function of the integration value (e_(d), e_(q)) isrepresented by Expression (18). $\begin{matrix}{{F\left( \begin{pmatrix}e_{d} \\e_{q}\end{pmatrix} \right)} = {\frac{1}{s^{2} + \left\{ {\left( {n - 1} \right)\omega} \right\}^{2}}\begin{pmatrix}s & {\left( {n - 1} \right)\omega} \\{{- \left( {n - 1} \right)}\omega} & s\end{pmatrix}{F\left( {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right)}}} & (18)\end{matrix}$

According to this expression, a diagonal component constitutes a bandpass filter by which a pass band has a rotational frequency ω, and anon-diagonal component constitutes a low pass filter by which a cutofffrequency has a rotational frequency ω. Therefore, there is thepossibility of robust properties with respect to the rotationalfrequency ω, performing transformation as follows can be considered.$\begin{matrix}{{F\left( \begin{pmatrix}e_{d} \\e_{q}\end{pmatrix} \right)} = {\frac{1}{s^{2} + {2{\zeta\left( {n - 1} \right)}\omega\quad s} + \left\{ {\left( {n - 1} \right)\omega} \right)^{2}}\begin{pmatrix}{s + {{\zeta\left( {n - 1} \right)}\omega}} & {\left( {n - 1} \right)\omega} \\{{- \left( {n - 1} \right)}\omega} & {s + {\zeta\left( {n - 1} \right)\omega}}\end{pmatrix}{F\left( {\begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right)}}} & (19)\end{matrix}$

In this expression, F( ) is a Laplace transform, s is a Laplaceoperator, and ζ is a constant corresponding to damping and 0<ζ<0.7 canbe considered as an appropriate value. $\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} = {{\left( {n - 1} \right){\omega\begin{pmatrix}\frac{- \zeta}{\left( {n - 1} \right)\omega} & {- 1} \\1 & \frac{- \zeta}{\left( {n - 1} \right)\omega}\end{pmatrix}}\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix}} + \begin{pmatrix}i_{d\quad r} \\i_{q\quad r}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}}} & (20)\end{matrix}$

Assuming that the above-described control system is a control system foran nth-order higher harmonic wave (ef) and Expressions (6) and (7) arecontrol systems for a fundamental wave (dq), a control system for thefundamental wave and the nth-order higher harmonic wave is as shown inFIG. 1 or 2. Further, a configuration which realizes this control systemis shown in FIG. 3.

In FIG. 1, processing with respect to a signal which has beentransmitted through a low pass filter in order to take out a fundamentalwave component corresponds to fundamental wave processing, andprocessing with respect to a signal which has been transmitted through ahigh pass filter in order to take out an nth-order higher harmoniccomponent corresponds to nth-order higher harmonic wave processing.

i_(dr) and i_(d), as well as i_(qr) and i_(q) of the fundamental wavetransmitted through the low pass filter, are input to a subtracter whereerror values (i_(dr)−i_(d)) and (i_(qr)−i_(q)) are calculated. Theobtained error values are each multiplied by K_(pd), thereby calculatingproportionals in the PI control over the fundamental wave. Furthermore,the error values (i_(dr)−i_(d)) and (i_(qr)−i_(q)) are subjected tointegration (1/s) and then multiplied by K_(id), thereby obtainingintegration terms of the PI control. Furthermore, these results areadded so that control voltages vd and vq of the fundamental wave can beobtained.

Moreover, i_(dr) and i_(d), as well as i_(qr) and i_(q) of the higherharmonic component transmitted through the high pass filter, are inputto the subtracter where error values (i_(dr)−i_(d)) and (i_(qr)−i_(q))are calculated. The obtained error values are multiplied by K_(p),thereby calculating proportionals in the PI control over the fundamentalwave. Additionally, the error values (i_(dr)−i_(d)) and (i_(qr)−i_(q))are subjected to integration (1/s) and then multiplied by K_(ie),thereby obtaining integration terms of the PI control. However, an adder(a subtracter) is provided before each integrator. The integration termof the d axis is multiplied by (n−1)ω and then subtracted from the errorof the q axis, and an obtained result is input to the integrator of theq axis. The integration term of the q axis is multiplied by (n−1)ω andthe added to the error of the d axis, and an obtained result is input tothe integrator of the d axis. Consequently, the control represented byExpression (15) and the like can be executed.

With such a configuration, the proportionals and the integration termsof the nth-order higher harmonic wave can be obtained with respect tothe d axis and the q axis, and the proportional and the integration termof the fundamental wave and the proportional and the integration term ofthe higher harmonic wave are added in the adders in accordance with thed axis and the q axis, thereby obtaining the control voltage vd of the daxis and the control voltage vq of the q axis.

In this manner, the PI control in the ef axis can be collectivelyperformed as the control of dq. It is to be noted that K_(pd)=K_(pq),K_(id)=K_(iq), K_(pe)=K_(pf) and K_(ie)=K_(if) are determined in thisexample.

FIG. 9 shows a processing part with respect to the higher harmonic wavein FIG. 1.

Further, in FIG. 2, a coefficient of proportional control is determinedas K_(pd)=K_(pe), and proportionals of the fundamental wave and thehigher harmonic wave are altogether calculated. That is, i_(dr) andi_(d) of the d axis are added without using a filter, and an obtainedresult is multiplied by K_(pd), thereby obtaining a proportional.Furthermore, i_(qr) and i_(q) of the q axis are added without using afilter, and an obtained result is multiplied by K_(pd), therebyobtaining a proportional.

FIG. 3 shows the overall configuration of the system. Theabove-described configurations of FIGS. 1 and 2 are employed in acurrent compensator. This current compensator outputs vd and vq asvoltage commands of the d axis and the q axis, and they are input to adq/uvw converting section. The dq/uvw converting section converts thevoltage command values of the dq axes into a switching command for aninverter which outputs each phase voltage driving voltage, and outputsthe switching command. The switching command is input to a PWM inverter.Motor driving voltages v_(u), v_(v) and v_(w) corresponding to vd and vqare supplied to respective phase coils of the three-phase motor 3 inaccordance with the PWM inverter switching command.

On the other hand, a rotor rotating position of the motor is detected bya position sensor. The position sensor may be of a type which detects achange in any other motor current of a hall element. A detected valuefrom the position sensor is input to an angle and angular velocitycalculator where an angle θ and an angular velocity ω of the rotor arecalculated from the rotor position detection result. This rotor angle θis input to the uvw/dq converter. Motor currents having a v phase and aw phase (which may be any two phases or three phases) detected by thecurrent detector are supplied to this uvw/dq converter where an excitingcurrent id and a torque current iq in the dq axis coordinate system arecalculated.

Moreover, id and iq from this uvw/dq converter and the angular velocityω from the angle and angular velocity calculator are supplied to thecurrent compensator. That is, a target value i_(dr) of the excitingcurrent, a target value iqr of the torque current, and the detectionresults id, iq and ω are input to this current compensator, and hence vdand vq are calculated by such configurations as shown in FIGS. 1 and 2.

With such configurations, the motor driving control taking the higherharmonic wave into consideration can be executed without performing thecoordinate transformation operation.

“dq Axis Current Control in αβ Coordinate System (PI Control Over dqAxis Coordinate System in αβ Coordinate System)”

When the PI control with the rotor fixed in the dq axis coordinatesystem is transformed into the αβ coordinate system with the statorfixed, the following expressions can be achieved. $\begin{matrix}{\begin{pmatrix}v_{\alpha} \\v_{\beta}\end{pmatrix} = {{K_{pd}\left\{ {\begin{pmatrix}i_{\alpha\quad r} \\i_{\beta\quad r}\end{pmatrix} - \begin{pmatrix}i_{\alpha} \\i_{\beta}\end{pmatrix}} \right\}} + {K_{id}\begin{pmatrix}e_{\alpha} \\e_{\beta}\end{pmatrix}}}} & (21) \\{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{\alpha} \\e_{\beta}\end{pmatrix}} = {{{\omega\begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix}}\begin{pmatrix}e_{\alpha} \\e_{\beta}\end{pmatrix}} + \begin{pmatrix}i_{\alpha} \\i_{\beta\quad r}\end{pmatrix} - \begin{pmatrix}i_{\alpha} \\i_{\beta}\end{pmatrix}}} & (22)\end{matrix}$

They correspond to Expressions (16) and (17), a difference in orderbetween the αβ coordinate system and the dq axis coordinate system is 1,and ω is adopted in place of (n−1)ω in Expression (17).

Therefore, FIG. 4 shows a block diagram for this control. Excitingcurrent and torque current commands (target values) i_(dr) and i_(qr)are input to the dq/αβ converter where these values are converted intoiα_(r) and iβ_(r). It is to be noted that a rotor angle θ is requiredfor this conversion, and this θ is also input to the dq/αβ converter.

iα_(r) and iα, along with iβ_(r) and iβ, are input to the subtracterwhere error values (iα_(r)−iα) and (iβ_(r)−iβ) are respectivelycalculated. The obtained error values are multiplied by K_(pd), therebycalculating proportionals in the PI control of the fundamental wave.Additionally, the error values (iα_(r)−iα) and (iβ_(r)−iβ) are subjectedto integration (1/s) and then multiplied by K_(id), thereby obtainingintegration terms of the PI control. However, an adder or a subtracteris provided before each integrator, and the integration term concerningthe α axis is multiplied by ω and then added to the error of the β axis,and the obtained result is input to the integrator of the β axis.Further, the integration term concerning the α axis is multiplied by ωand then subtracted from the error of the β axis, and the obtainedresult is input to the integrator of the β axis. Consequently, thecontrol represented by Expression (15) and the like can be executed.

With such a configuration, the proportional and the integration term ofthe PI control in the dq axis coordinate system can be obtained withrespect to the αβ coordinate system, and the control voltage vα of the αaxis and the control voltage vβ of the β axis an be obtained.

FIG. 5 shows the entire control system. This configuration is basicallythe same as that shown in FIG. 3. iα_(r), iβ_(r), iα, iβ and ω are inputto the current compensator, and vα and vβ are obtained by theconfiguration shown in FIG. 4. vα and vβ are input to the αβ/uvwconverter where commands of respective phases u, v and w are created,and the motor is thereby driven. Furthermore, motor currents i_(v) andi_(w) are converted into iα and iβ in the uvw/aβ converter.

In this manner, the PI control in the dq axis coordinate system can berealized in the αβ coordinate system.

“Higher Harmonic Control Method in dq Coordinate System (General Filterof ef Coordinate System in dq Coordinate System)”

In the above, an example in which the PI control (the control whichcalculates proportionals and integration terms of errors) in the ef axiscoordinate system is carried out in the dq axis coordinate system wasdescribed. Next, an example which realizes in the dq axis coordinatesystem a general filter in the ef coordinate system (the coordinatesystem of n rotations) will be described.

It is to be noted that although in the following description the orderof the filter is the fourth order, the order of the filter can bereadily extended to the sixth order, the eighth order, etc. It is to benoted that m=n−1 is determined.

First, transformation into the dq axis coordinate system by thefourth-order filter corresponding to Expressions (10) to (12) can berepresented as follows. $\begin{matrix}{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{T^{\prime}\left( {m\quad\theta} \right)}\begin{pmatrix}v_{e} \\v_{f}\end{pmatrix}}} & (23) \\{\begin{pmatrix}i_{d} \\i_{q}\end{pmatrix} = {{T^{\prime}\left( {m\quad\theta} \right)}\begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}}} & (24) \\{\begin{pmatrix}e_{d} \\e_{q}\end{pmatrix} = {{T^{\prime}\left( {m\quad\theta} \right)}\begin{pmatrix}e_{e} \\e_{f}\end{pmatrix}}} & (25) \\{\begin{pmatrix}i_{r} \\i_{s}\end{pmatrix} = {{T^{\prime}\left( {m\quad\theta} \right)}\begin{pmatrix}i_{g} \\i_{h}\end{pmatrix}}} & (26) \\{\begin{pmatrix}e_{r} \\e_{s}\end{pmatrix} = {{T^{\prime}\left( {m\quad\theta} \right)}\begin{pmatrix}e_{g} \\e_{h}\end{pmatrix}}} & (27)\end{matrix}$

On the other hand, the fourth-order filter in the ef axis coordinatesystem can be represented as follows. $\begin{matrix}{\begin{pmatrix}v_{e} \\v_{f}\end{pmatrix} = {{K_{p}\quad\left\{ {\begin{pmatrix}i_{er} \\i_{fr}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}} \right\}} + {K_{i}\quad\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}}}} & (29) \\{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}} = {{B\quad\left\{ {\begin{pmatrix}i_{er} \\i_{fr}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}} \right\}} + {A\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}}}} & (30)\end{matrix}$

The general filter of the ef coordinate system represented byExpressions (29) and (30) is transformed into the dq coordinate system.In this transformation, φ2×2 is a zero matrix of two rows and twocolumns. $\begin{matrix}{\begin{pmatrix}v_{d} \\v_{q}\end{pmatrix} = {{{T^{\prime}\left( {m\quad\theta} \right)}\quad K_{p}{T\left( {m\quad\theta} \right)}\quad\left\{ {\begin{pmatrix}i_{dr} \\i_{qr}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\}} + {{T^{\prime}\left( {m\quad\theta} \right)}\quad{K_{i}\begin{pmatrix}{T\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T\left( {m\quad\theta} \right)}\end{pmatrix}}\quad\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}}}} & (31) \\{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}} = {\frac{\mathbb{d}}{\mathbb{d}t}\left\{ {\begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix}\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}} \right\}}} & (32) \\{\quad{= {{\frac{\mathbb{d}}{\mathbb{d}t}\left\{ \begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix} \right\}\quad\begin{pmatrix}{T\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T\left( {m\quad\theta} \right)}\end{pmatrix}\quad\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}} +}}} & \quad \\{\quad{\begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix}\quad\frac{\mathbb{d}}{\mathbb{d}t}\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}}} & \quad \\{\quad{= {{\frac{\mathbb{d}}{\mathbb{d}t}\left\{ \begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix} \right\}\quad\begin{pmatrix}{T\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T\left( {m\quad\theta} \right)}\end{pmatrix}\quad\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}} +}}} & \quad \\{\quad{\begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix}\quad\left\lbrack {{B\left\{ {\begin{pmatrix}i_{er} \\i_{fr}\end{pmatrix} - \begin{pmatrix}i_{e} \\i_{f}\end{pmatrix}} \right\}} + {A\quad\begin{pmatrix}e_{e} \\e_{f} \\e_{g} \\e_{h}\end{pmatrix}}} \right\rbrack}} & \quad \\{\quad{= {{\left( \frac{\mathbb{d}\theta}{\mathbb{d}t} \right)\begin{pmatrix}\begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix} & \phi_{2 \times 2} \\\phi_{2 \times 2} & \begin{pmatrix}0 & {- 1} \\1 & 0\end{pmatrix}\end{pmatrix}\quad\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}} +}}} & \quad \\{\quad{{\begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix}\quad B\quad{T\left( {m\quad\theta} \right)}\quad\left\{ {\begin{pmatrix}i_{dr} \\i_{qr}\end{pmatrix} - \begin{pmatrix}i_{d} \\i_{q}\end{pmatrix}} \right\}} +}} & \quad \\{\quad{\begin{pmatrix}{T^{\prime}\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T^{\prime}\left( {m\quad\theta} \right)}\end{pmatrix}\quad A\quad\begin{pmatrix}{T\left( {m\quad\theta} \right)} & \phi_{2 \times 2} \\\phi_{2 \times 2} & {T\left( {m\quad\theta} \right)}\end{pmatrix}\quad\begin{pmatrix}e_{d} \\e_{q} \\e_{r} \\e_{s}\end{pmatrix}}} & \quad\end{matrix}$

In Expression (32), the first term in the right side member is a partcorresponding to an interference of the integration term, and the secondand third terms are a part corresponding to the regular filter. That is,in case of the above-described PI control, this corresponds to a partwhere (n−1)ω is multiplied and a result is added to or subtracted froman error of the other axis. As described above, in this example, sincethe first term in the right side member exists, the appropriate controlcan be achieved in cases where the nth-order filter is realized in thedq axis coordinate system.

Moreover, in this example, the filter on the ef axis coordinate systemis realized on the dq axis coordinate system. However, the filter on onecoordinate system can be realized with another coordinate by the sametechnique.

SIMULATION EXAMPLE

A simulation result when the sixth-order higher harmonic wave is appliedto a back electromotive force in a motor voltage equation represented bythe dq axes will now be described with reference to FIGS. 6 to 8. Inthese drawings, the top portion represents an axis current, the lowerportion represents an axis current, and the right side is an expandedview of the left side.

FIG. 6 shows a conventional technique by which the PI control isexecuted with respect to a fundamental wave in the dq axes, and it canbe understood that a higher harmonic component cannot be suppressed.FIG. 7 shows a technique by which the dq axes are prepared in accordancewith each higher harmonic wave, and FIG. 8 shows a technique accordingto this embodiment which also performs the control over a higherharmonic wave having a frequency six times that of a rotor as thecontrol of the dq axis coordinate system, in which the control techniqueitself is transformed into the dq axis coordinate system. As describedabove, it can be understood that the technique according to thisembodiment or the method which prepares the coordinate system inaccordance with each higher harmonic wave can suppress a harmonic wavesix times greater than possible with the conventional method.

As described above, according to this embodiment, the PI control in theef coordinate system which realizes a rotational frequency which is ntimes that of the rotor can be carried out for control in a dq axiscoordinate system. Further, the nth-order filter in one coordinatesystem can be handled as a filter on any other coordinate system whichrelatively rotates with respect to the former coordinate. Therefore, inthe motor driving control, the control taking a higher harmonic wave orthe like into consideration can be achieved without performingcoordinate transformation of all variables each time.

1. A control device for an alternating-current motor including a rotorand a stator, wherein in one coordinate system of arbitrary rectangularcoordinate systems including a coordinate system fixed to the stator, acoordinate system fixed to the rotor and a coordinate system whichrotates at a rotational frequency which is n times (n is an integerwhich is not 0 or 1) that of the rotor, a filter on any other coordinatesystem is defined, and driving of the motor is controlled by utilizingthe filter.
 2. A control device for an alternating-current motorincluding a rotor and a stator, the control device comprising: afundamental wave current control circuit which obtains a current controloutput which controls a fundamental wave component of a motor current inan axis coordinate system which rotates in synchronization with therotor with respect to a d axis current which is mainly an excitingcurrent component of a phase current of the alternating-current motorand a q axis current which is mainly a torque current component of thesame; a higher harmonic current control circuit which controls an e axiscurrent and an f axis current, the e axis current and the f axis currenthaving a frequency which is an integer multiple of a frequency of thefundamental wave component of the alternating motor, the higher harmoniccurrent control circuit realizing the e and f axes current controls onthe d axis current control and the q axis current control; an additioncircuit which adds an output from the fundamental wave current controlcircuit and an output from the higher harmonic current control circuit;and an inverter circuit which receives an output from the additioncircuit and outputs a motor driving current, wherein PI control in thehigher harmonic current control circuit is also executed as currentcontrol on the d and q axes.
 3. The apparatus according to claim 2,wherein the higher harmonic current control circuit comprises: a firstoperation unit which performs subtraction or addition with respect to aconstant multiple of an output from an f axis current error integrationcontroller and an e axis current error; a second operation unit whichperforms addition or subtraction with respect to a constant multiple ofan output from an e axis current error integration controller and the eaxis current error; an e axis current error proportional controllerwhich subjects an output from the first operation unit to proportionalmultiplication; an f axis current error proportional controller whichsubjects an output from the second operation unit to proportionalmultiplication; an e axis higher harmonic controller which adds aconstant multiple of the e axis current error and an output from the eaxis current error proportional controller; and an f axis higherharmonic controller which adds a constant multiple of the f axis currenterror and an output from the f axis current error proportionalcontroller; wherein the e axis current error integration controllersubjects an output from the first operation unit to integration; and thef axis current error integration controller subjects an output from thesecond operation unit to integration and proportional multiplication. 4.The control device for an alternating-current motor according to claim2, wherein the higher harmonic current control circuit realizes on the dand q axes PI control on the e and f axes by utilizing expressionsobtained by transforming expressions of the PI control on the e and faxes into expressions on the d and q axes.
 5. (canceled)
 6. A currentcontrol circuit which separates an α phase current and a β phase currentas current components of axes which are fixed to a stator and orthogonalto each other with respect to an alternating-current motor including arotor and the stator, and controls the respective phase currents basedon an α phase current error and a β phase current error which are errorsfrom command values of motor currents of the α phase current and the βphase current, the current control circuit comprising: an α phaseproportional unit which multiplies the α phase current error by apredetermined proportional coefficient to obtain an α phase proportionalcontrol component; an α phase integrator which integrates a differencevalue between the α phase current error and a coefficient multiple basedon a rotational frequency of the rotor as an output from a β phaseintegrator; a β phase integrator which integrates an added value of theβ phase current error and a coefficient multiple based on a rotationalfrequency as an output from the α phase integrator; an α phase voltagecommand unit which adds an α phase integration control componentobtained by multiplying an output from the α phase integrator by apredetermined proportional coefficient and an α phase proportionalcontrol component as an output from the α phase proportional unit, andoutputs an α phase voltage command; a β phase voltage command unit whichadds a β phase integration control component obtained by multiplying anoutput from the β phase integrator by a predetermined proportionalcoefficient and a β phase proportional control component as an outputfrom the β phase proportional unit, and outputs a β phase voltagecommand; and an inverter circuit which drives the alternating-currentmotor based on the α phase voltage command and the β phase voltagecommand from the α phase voltage command unit and the β phase voltagecommand unit.
 7. The control device for an alternating-current motoraccording to claim 3, wherein the constants are the same value and thevalue is a product of n−1 and a rotation angular velocity based on anelectrical angle, wherein n is a rotation order of the e and f axeswhich rotate at a rotation frequency which is n times that of the d andq axes, wherein n is an integer which is not 0 or 1.